The dielectric properties of tumour cells are known to differ from normal blood cells, and this difference can be exploited for label-free separation of cells. Conventional measurement techniques are slow and cannot identify rare circulating tumour cells (CTCs) in a realistic timeframe. We use high throughput single cell microfluidic impedance cytometry to measure the dielectric properties of the MCF7 tumour cell line (representative of CTCs), both as pure populations and mixed with whole blood. The data show that the MCF7 cells have a large membrane capacitance and size, enabling clear discrimination from all other leukocytes. Impedance analysis is used to follow changes in cell viability when cells are kept in suspension, a process which can be understood from modelling time-dependent changes in the dielectric properties (predominantly membrane conductivity) of the cells. Impedance cytometry is used to enumerate low numbers of MCF7 cells spiked into whole blood. Chemical lysis is commonly used to remove the abundant erythrocytes, and it is shown that this process does not alter the MCF7 cell count or change their dielectric properties. Combining impedance cytometry with magnetic bead based antibody enrichment enables MCF7 cells to be detected down to 100 MCF7 cells in 1 ml whole blood, a log 3.5 enrichment and a mean recovery of 92%. Microfluidic impedance cytometry could be easily integrated within complex cell separation systems for identification and enumeration of specific cell types, providing a fast in-line single cell characterisation method.